To simplify the expression \(-5\sqrt{10}(2+\sqrt{14})\), follow these steps:

1. **Distribute** \(-5\sqrt{10}\) to both terms inside the parentheses:
   \[
   -5\sqrt{10} \cdot 2 + (-5\sqrt{10} \cdot \sqrt{14})
   \]

2. **Multiply** each term:
   - First term: \(-5\sqrt{10} \cdot 2 = -10\sqrt{10}\)
   - Second term: \(-5\sqrt{10} \cdot \sqrt{14}\)

3. **Simplify the second term** by multiplying the square roots:
   \[
   \sqrt{10} \cdot \sqrt{14} = \sqrt{10 \times 14} = \sqrt{140}
   \]
   Simplify \(\sqrt{140}\):
   \[
   \sqrt{140} = \sqrt{4 \times 35} = 2\sqrt{35}
   \]
   So the second term becomes:
   \[
   -5 \times 2\sqrt{35} = -10\sqrt{35}
   \]

4. **Combine the simplified terms**:
   \[
   -10\sqrt{10} - 10\sqrt{35}
   \]

Thus, the expression \(-5\sqrt{10}(2+\sqrt{14})\) simplifies to:

\[
-10\sqrt{10} - 10\sqrt{35}
\]

Would you like a detailed explanation of any of these steps?

Here are 5 related questions for further practice:
1. Simplify \(\sqrt{20} + \sqrt{45}\).
2. Simplify \(3\sqrt{5}(2 + \sqrt{3})\).
3. Expand and simplify \((2 + \sqrt{3})(2 - \sqrt{3})\).
4. Simplify \(\sqrt{18} + 2\sqrt{8}\).
5. Simplify \(7\sqrt{2} \times 3\sqrt{6}\).

**Tip:** When simplifying square roots, always look for factors that are perfect squares to simplify the expression further.

Learn how to simplify the expression -5√10(2+√14) step-by-step with detailed explanations. This problem involves simplifying radicals and applying distributive property. Suitable for high school students.

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